Finite Group Databasebeta

← #14656274

Subgroups — #14656274

Order 2816.

474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079961C211yesmaximal, characteristic
2#13078421C212yesmaximal
3#13067072C212yesmaximal
4#13066491C211yesmaximal, characteristic
5C11×#1984C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7#10623001C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10#10622838—22no—
11#10622729—22no—
12#10622635—24no—
13#10622634—22no—
14#10622633—22no—
15#10622577—22no—
16#10622537C2212yes—
17#10622463—22no—
18#10622462—22no—
19C11×#336—22no—
20#10622094—24no—
21C22×Q8×C11D411yescharacteristic
22C22×C8×C11—21no—
23C22×C8×C11D412yes—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11—21no—
29C2×C42×C11C2311yescharacteristic
30#66979—22no—
31#66977—22no—
32#66977—22no—
33C2×#4318—22no—
34C2×Dic44—22no—
35#66923—22no—
36#66922D412yes—
37#66922D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C4×C8×C11—22no—
42#66899—24no—
43#66899—24no—
44#66882—22no—
45#66880—24no—
46#66872—24no—
47#66871—24no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)D414yes—
50#10259—111nomaximal, Sylow
51C2×Q8×C11—21no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11Q1612yescomplemented
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C2×Dic22—22no—
61C2×Dic22—22no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—42no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—42no—
69C42×C11—41no—
70C42×C11—41no—
71C42×C11C2×D412yes—
72C42×C11C2×D412yes—
73C22⋊Dic11—42no—
74C4⋊Dic11—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80C4×Dic11—42no—
81#4318—42no—
82#4318—42no—
83C2×C11⋊C8—24no—
84Dic44—82no—
85#3249—111no—
86#3078—112no—
87#1984D1111yescharacteristic
88#1493—112no—
89#1292—111no—
90C23×C11#12111yescharacteristic
91Q8×C11—24no—
92Q8×C11—42no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11#12012yes—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11#12112yes—
104C2×C4×C11#12711yescharacteristic
105C2×C4×C11C2×Q1611yescharacteristic
106C2×C4×C11#13511yescharacteristic
107C2×C4×C11#13712yes—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—44no—
111Dic22—42no—
112Dic22—42no—
113C8×C11—42no—
114C8×C11—42no—
115C11⋊C8—44no—
116#533—112no—
117C2×C4×Q8C2×D1111yescharacteristic
118#479—224no—
119#477—222no—
120#477—222no—
121#475—222no—
122#467—222no—
123#462—222no—
124#428—222no—
125#423—112no—
126C2×C4⋊C8C2×D1111yescharacteristic
127#419—222no—
128C2×C4×C8C2×D1111yescharacteristic
129#336—22no—
130Q8⋊C8—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11#39211yescharacteristic
134C22×C11#46711yescharacteristic
135C22×C11#47011yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—42no—
139C4×C11—81no—
140C4×C11#45112yes—
141C4×C11#45212yes—
142C4×C11#45511yescharacteristic
143C4×C11#45611yescharacteristic
144Dic11—82no—
145Dic11—82no—
146C22×Q8D4411yescharacteristic
147C2×Q16—222no—
148C2×M16—222no—
149C22×C8—21no—
150C22×C8C22⋊D1112yes—
151C4⋊Q8—112no—
152C4⋊Q8—112no—
153#125—222no—
154C22⋊Q8—222no—
155C22⋊Q8—222no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—222no—
159C4×Q8—222no—
160#117—222no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4411yescharacteristic
163C2×C42—21no—
164C2×C42C22×D1111yescharacteristic
165#107—224no—
166#107—222no—
167#106—224no—
168C4⋊C8—22no—
169C4⋊C8—114no—
170C4⋊C8—222no—
171#103—224no—
172#103—224no—
173#103—224no—
174C4×C8—22no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#200111yescharacteristic
178C2×C11#200711yescharacteristic
179C2×C11#201711yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—222no—
184C2×Q8—222no—
185C2×Q8Dic4412yescomplemented
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C2×D4411yescharacteristic
189C22×C4#433911yescharacteristic
190C22×C4C2×C22⋊D1111yescharacteristic
191Q16—882no—
192M16—442no—
193M16—442no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—42no—
199C2×C8—224no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—222no—
206C4⋊C4—442no—
207C4⋊C4—442no—
208C22⋊C4—442no—
209C42—41no—
210C42—41no—
211C42—442no—
212C42D4×D1112yes—
213C42D4×D1112yes—
214C11#1025911yescharacteristic, complemented, Sylow
215C23#6698311yescharacteristic
216Q8—24no—
217Q8—42no—
218Q8—444no—
219Q8—442no—
220Q8—442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4#6693512yes—
232C2×C4#6693712yes—
233C2×C4#6695711yescharacteristic
234C2×C4C2×Dic4411yescharacteristic
235C2×C4#6696212yes—
236C2×C4#6699011yescharacteristic
237C2×C4#6699311yescharacteristic
238C8—42no—
239C8—42no—
240C8—444no—
241C22—21no—
242C22—21no—
243C22#1062257311yescharacteristic
244C22#1062272911yescharacteristic
245C22#1062275011yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—81no—
250C4—882no—
251C4—882no—
252C4#1062234612yes—
253C4#1062235212yes—
254C4#1062267411yescharacteristic
255C4#1062270811yescharacteristic
256C2—21no—
257C2—21no—
258C2#1306962611yescharacteristic
259C2#1306966211yescharacteristic
260C2#1306972011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10259
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1984

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
54. C2×Q8×C11Q16semidirect
185. C2×Q8Dic44semidirect
214. C11#10259semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130799612
#130784212
#130670722
#130664912
C11×#19842
#1025911